Astronomy

Binary star not exceeding Roche Lobe?

Binary star not exceeding Roche Lobe?


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Is it possible that a binary star doesn't exceed its Roche lobe and so when the second star becomes a red giant, instead of accreting some of its plasma onto the white dwarf that it becomes a white dwarf itself which causes there to be no supernova?


Of course this is possible. Whether it will fill its Roche lobe depends on the masses and radii of the stars and the distance between the stars. If the distance is big enough then the second (less massive) star will not fill its Roche lobe and continue evolving as a single star would. The (large) majority of binaries will fall in this category, only close binaries will evolve into cataclysmic variables.

For instance the Alpha Centauri/Proxima Centauri system will not evolve into a system where mass transfer takes place via the Roche lobes as the distance between Alpha Cen A/B and Proxima Centauri is much too big.

Even when the stars are very close, a supernova might not occur if the masses of the stars are low. The supernova occurs when the mass of the existing white dwarf increases (because of the accretion) to a mass surpassing the Chandrasekhar limit (1.4 solar masses). If the transferred mass is too low then no supernova will happen.


Roche lobes

Roche lobes An imaginary surface around a star. Each star in a binary system can be pictured as being surrounded by a tear-shaped zone of gravitational influence, the Roche lobe. Any material within the Roche lobe of a star can be considered to be part of that star.

If the two components are in a close binary and do not fill their Roche lobes, the system is considered a detached binary. In a semidetached binary, one star fills its Roche lobe and mass transfer occurs. In a contact binary, both stars fill their Roche lobes.

Stars that remain within their own roche lobes are termed detached binaries, while semidetached binaries have one star (often a red giant) filling its Roche lobe.

If you have two stars that are both smaller than their

, then that type of binary is referred to as a detached binary, and the stars will not have a direct influence on each other's evolution.

Since the outer gas envelopes of the stars are in contact (overflowing their

), they essentially share a common photosphere despite having two distinct nuclear-burning cores. Indeed, Stars B and C are separated by only some 0.

In most contact binaries one component is larger than the other. In this kind of system both stars fill their respective

, and become so-called overcontact binaries with a common gaseous envelope.

"Instead, if the stars continue to evolve homogeneously and keep shrinking within their

, coalescence can be avoided.

contact binary A binary star system in which both stars have expanded to fill their

and the surfaces of the two stars merge. The binary system now consists of two nuclear burning stellar cores surrounded by a continuous common envelope.

Common Envelope - A stage in the evolution of a close pair of stars in which matter shed by one of the stars fills the region just outside the

of the two stars
Conduction - The transfer of heat by means of direct collisions between adjacent atoms, molecules, or ions .

The first equipotential surface for two massive bodies describing circular orbits around one another which forms a figure eight enclosing the two objects. The

are the two lenticular volumes enclosing the two bodies. [H76]
Rods .

As the red giant expands, the material in its outer layers don't expand out in any direction due to the proximity of the nearby white dwarf, so the material is funneled toward it. This is due to the constraints of the

. Eventually the material on the white dwarf will ignite as a nova.

If one of the stars is big enough to transfer mass through the Lagrange point then the system is a semidetached binary. If both stars fill their

then the system is known as a contact binary. Such a system is almost more like a double-core, figure 8 shaped star.


Overflow in Binary Stars

When we think of a star's shape, we normally think of the Sun, which is a slightly flattened sphere. Most stars are an equilibrium of pressure, self-gravity, and rotation, and a flattened sphere is the the natural shape that these opposing forces create. If a star is in a close binary system, however, pressure is in equilibrium not only with the star's own rotation and gravity, but also with the rotation of the binary system and the gravity of the companion star. These additional bits of physics distend the star in the direction of the companion star. At its weakest, the effect is a slight tidal distortion, much like the distortion of Earth's oceans by the Sun and the Moon, that elongates the star, but at its most extreme, the effect molds the star into the shape of a raindrop, with its sharp point facing the companion star. This distortion of the photosphere in the direction of the companion is called the Roche lobe.

Tidal forces are a form of friction. In the Earth-Moon system, tidal friction caused the rotation of the Moon to synchronize with its orbit around Earth, so that we only see one side of the Moon. Tidal friction is causing Earth's rotation to slow. We see a similar effect in a close binary star a star's Roche lobe dissipates rotational energy, driving the rotation period of the star to the orbital period. If the orbit is eccentric, the tidal distortion strengthens and then weakens over an orbit, causing a dissipation of orbital energy and making the orbit more circular.

There is a maximum size to a star's Roche lobe. For a star in a circular orbit, this maximum size is set by a point of unstable equilibrium between it and its companion star. This point is called the inner Lagrange point it is often referred to as the L1 point. An object at the inner Lagrange point would stay on a line between the two stars in the system, maintaining a fixed separation with each star. If the object were displaces from this point towards one of the stars, that object would orbit that star. A star's Roche lobe reaches its maximum possible size when its touches the inner Lagrange point any larger, and the star's atmosphere flows onto the companion star. A star that touches the inner Lagrange point is said to fill its Roche lobe. When a star becomes bigger, so that its atmosphere begins to flow onto the companion star, the star is said to undergo Roche lobe overflow. Roche lobe overflow alters both the orbit and the structure of the overflowing star.

As you would expect, a star's structure is altered when it undergoes Roche lobe overflow. The structure of the star changes to compensate for the reduction in gravitational force within the star and the removal of the star's coolest outer layers. The star reacts by mimicking the structure of a more-evolved star. The core of the star shrinks, but the outer layers expand, with the overall effect that the star puffs up.

How mass flow changes the orbits of a binary star system depends on whether the overflowing star is more or less massive than its companion. If the overflowing star is less massive, the distance between the stars and the orbital period of the binary increase over time, but if it is more massive, the distance and the orbital period decrease. This is a consequence of conservation of angular momentum. As mass flows from one star to the other, changing the mass of each and shifting the center of mass of the system, the system's size changes to preserve its angular momentum.

Why this occurs is easy to see if we start with two stars of equal mass. The center of mass for the system is halfway between the stars, and each star carries half of the angular momentum of the system. The angular momentum carried by each star is 2 M R 2 /P, where M is the mass of the star, R is the distance to the center of mass, and P is the orbital period. If we then move almost all of the mass of one star to the other, but kept the angular momentum fixed, we would find that the system's center of mass is very close to the center of the large star. This short distance makes the angular momentum carried by the massive star much less than that carried by the two stars before we mass transfer. This means that the bulk of the angular momentum must be carried by the small star, much as in the Jupiter-Sun system, the bulk of the angular momentum of the orbit is carried by Jupiter, because the Sun's offset from the center of mass is so small. But for the small star to carry as much angular momentum as the previous system, the distance of this star from center of gravity must be much greater than in the previous system.

For two stars with much different masses, the orbital period is related to the separation between the stars as P 2 is proportional to D 3 . Because the distance to the center of mass for the small star is effectively the separation between stars, the angular momentum carried by the small star is proportional to R 1/2 . Because the angular momentum is such a weak function of the separation between the stars, the separation between the stars must increase dramatically for the small star to carry the same angular momentum as the original system.

The position of the inner Lagrange point moves towards the star losing mass as mass exchange continues. When two stars have equal mass, the inner Lagrange point is precisely between the two stars, coincident with the center of mass of the system. If mass is transferred from one of these stars to the other, the inner Lagrange point moves in the direction of the smaller star. The question is whether this motion towards the small star is countered by the increase in the binary star separation. It turns out that while the distance from the inner Lagrange point to the small star decreases relative to the distance from the inner Lagrange point to the large star as the small star loses mass to the large star, the absolute distance from the small star to the inner Lagrange point increases. This means that as the smaller star loses mass to the larger star, its maximum Roche lobe increases in volume. Conversely, if mass is transferred from the large star to the small star, the maximum Roche lobe of the large star decreases in volume, because the inner Lagrange point moves toward the large star as the distance between the stars gets smaller.

We find that an overflowing star is unable to expand enough to keep its Roche lobe filled when that star is less massive than its companion. If only these mechanisms?the expansion of the maximum Roche lobe and the expansion of the star?were present, Roche lobe overflow could never occur, because the mass transfer would cause the star to cease overflowing its Roche lobe, bringing mass transfer to a halt. But there are other, slower processes that shrink the distance between the stars. Both a stellar wind and gravitational waves carry orbital energy and angular momentum out of the system, causing the binary orbit to shrink and the smaller star to fill its Roche lobe. Once mass transfer starts, the decay of the orbit comes into equilibrium with the expansion from mass transfer. In this way, the system transfers mass steadily from the smaller star to the larger star.

The converse occurs if the overflowing star is more massive than its companion. In this case, the separation between the stars shrinks, as does the distance from the inner Lagrange point to the massive star. Add to this the expansion of the massive star as mass is removed, and we have a system that is unstable to mass flow. Once the massive star begins overflowing its Roche lobe, the rate of flow increases rapidly, until so much mass has been pulled onto the companion star that both stars fill their Roche lobes. The continued expansion of the massive star then enshrouds both stars in a common envelope of gas within this new, single star, two cores rapidly orbit each other, rapidly coming closer to each other as the orbit loses energy to the common envelope.


Binary star not exceeding Roche Lobe? - Astronomy

There are four categories of binary stars, depending on how close the stars are to one another.

Distant Binaries orbit many astronomical units from each other Many stellar systems, such as Alpha Centauri A+B, are distant binary systems, and many include planets. As a rough 'rule of thumb', distant binary stars can have planets orbiting one, or both, stars, but only if the planets orbit at a distance of less than one third of the minimum distance between the stars (this can vary significantly in the case of stars with high eccentricity values, or systems where one star is much more massive than the other). Planets that orbit just one star in a binary pair are said to have "S-type" orbits, whereas those that orbit around both stars have "P-type" or "circumbinary" orbits.

Close Binaries orbit within a few stellar diameters of each other, but are not in direct physical contact. Close binaries can have a system of planets orbiting around both stars (in so-called "P-type" orbits), but only if the orbit of the closest planet orbit is wider than more than about 3 x the distance between the stars (more on close binaries here). Both Distant Binaries and Close Binaries are known as Detached Binaries because neither star fills its Roche Lobe.

Semidetached binaries are binary stars where one of the components fills the binary star's Roche lobe and the other does not. There is a net flow of matter from the star which does fill its Roche lobe to the other star. In some cases this flow of matter can cause extreme or cataclysmic variations in the brightness of the recipient star.

Contact Binaries These stars orbit close enough to be in physical contact, and often share a common gaseous envelope (more on contact binaries here).


Types of Binary Star Systems

A greater percentage of systems are multiple star systems, meaning that they are systems containing two or more stars, and in particular, binary star systems, which specifically contain two stars, are exceptionally common. When we can see both of the stars, they are called visual binaries, and if the plane of their orbit happens to coincide with our line of sight, such that they pass in front of each other, they are called eclipsing binaries. This situation allows us to gather important information about the system, and is actually one of the best ways to detect them in the first place, as we can chart the reliably periodic change in luminosity first as the larger star passes in front of the smaller, and then as the smaller star passes in front of the larger, in cyclical fashion.

But beyond this, we also know that stars come in many different varieties. Therefore, the possible combinations that exist for the two types of stars that comprise a binary system are even more numerous. What are the most interesting combinations we have been able to find for types of binary star systems, and what can they teach us about the universe? Certainly, there are many binary systems that involve very sun-like stars orbiting each other at quite a distance. An example of this is Alpha Centauri A and B, which we examined in a previous tutorial.

But a far more interesting case involves close binary systems. This is when the stars are very close together, orbiting around their center of mass quite rapidly. Sometimes they are so close that the gravitational distortion produced causes their stellar atmospheres to exchange material, or they could even be so close that they are in direct contact with one another, such as this system with two large, hot, main sequence stars practically overlapping. This is most fascinating when one star is a compact object, like a white dwarf star, neutron star, or black hole, as this object will begin to pull matter away from the other object in the system until a dramatic event occurs. If a white dwarf is causing the accretion of gas from another star, it becomes a cataclysmic variable star, where the incoming gas gets very hot and emits radiation.

We sometimes call such an object a vampiric star, as it is almost as though it is sucking the essence out of its companion star like a vampire. If instead the compact object is a neutron star or black hole, this is called an X-ray binary, which can be either a low-mass or high-mass X-ray binary depending on the mass of the donor star, which is the other star in the system, feeding the compact object with material. One fascinating binary system is called AR Scorpii. This is a binary pulsar, which consists of a white dwarf-pulsar about the size of Earth, and a red dwarf star. Pulsars are highly magnetized objects that emit powerful beams of radiation in a rapid, periodic manner.

Typically pulsars are neutron stars, but sometimes they can be white dwarfs as well, though being much less compact than neutron stars they rotate more slowly. AR Scorpii contains the first object of this type that was ever discovered. We should note that binary systems can have complicated evolutions. Take for example a binary system with two fairly large main sequence stars, which form with around 15 and 20 solar masses respectively.

We know that stars of this size evolve rapidly, since the inward gravitational pressure is so strong that fusion occurs at a furious pace, burning through the hydrogen in the core much faster than in smaller stars. Eventually one star enters a phase of expansion and will exceed its Roche lobe, meaning that it juts far enough into the gravitational field of the other star that one will begin to pull material away from the other. This material may form an accretion disc, as we saw previously, but it can also be absorbed through direct impact, as shown here. We see the blue star acting as the vampiric star, rotating faster and flattening out.

We also see that an enormous percentage of the other star’s mass is being transferred in the process, actually the majority of its mass. This star is now so much more massive that fusion increases even more dramatically, which generates a stellar wind that causes the other star to become very small. Eventually this star will go supernova and leave a tiny neutron star behind, potentially escaping the system altogether. The vampiric star will then reach a red supergiant phase where it expands immensely, after which it too will go supernova and leave a neutron star behind. So we can see that stellar evolution is much more complicated in binary systems due to the influence each star has on the other. There are so many fascinating systems out there, not just binary systems, but triple-star systems and beyond.


Binary star not exceeding Roche Lobe? - Astronomy

We present the first spectroscopic investigation of the short-period (P=0.309614d) mass-exchanging binary system V361 Lyr. From observations over two complete orbits, we show that the system is double-lined, with the stars having minimum masses of m_1sin^3i=1.25+/-0.03 Msolar and m_2sin^3i=0.87+/-0.03 Msolar. The mass ratio m_2/m_1=0.69+/-0.02 and the projected semimajor axis of the relative orbit is asini=2.47+/-0.05 Rsolar. The spectral type of the primary component is estimated to be F8-G0. The Hα line profile clearly shows two absorption components when the system is at its brightest and bluest stage, around orbital phases 0.35-0.45. The published V and I light curves are analysed with light2 to show that the primary component (T=6200K) fills its Roche lobe, whilst the secondary (T=4500K) is detached and fills

57 per cent of the available Roche volume. Eclipse maps of both stellar surfaces are derived via dots from light curves obtained in 1988, 1989 and 1992. These show that the secondary has a persistent elongated hot structure on its equator with an estimated temperature of 10000K that is consistent with the expectations of a theoretical mass transfer stream leaving the primary at its inner Lagrangian point and falling on to the secondary. The accretion luminosity of


Binary Star Questions

I am doing a school project on binary star, so I was hoping that some of the folks on this subreddit would know the answers to my questions. If you have a good website to link me to, I would love that.

If you have an answer, a source is greatly appreciated.

Is one of the stars in a binary system bigger than the other generally?

I know they can vary in size as they can be average or massive, so what is a size range for average stars and range for massive stars?

What is the lifetime range of an average binary star system and a massive binary star system?

Is there any special thing that happens during the stellar nebula stage to form 2 stars?

Is one of the stars in a binary system bigger than the other generally?

The odds of two stars being exactly the same size is basically zero, so really, you need to specify how similar you want to stars' masses/radii to be in order to call them the same. Typically, we refer to stars with masses within 5% of each other as 'twins'. This behemoth of a paper has a lot of information about binary stars' properties, although there is still some uncertainty which comes from the difficulty of measuring every property of every binary star. The figure youɽ be most interested in is figure 2, on page 5. The mass ratio, q, is the mass of the smaller star divided by that of the larger star, so it is always between 0 and 1, with q > 0.95 indicating stellar twins. There are three parameters which describe the distribution of q: γ_smallq, γ_largeq, and F_twin. These are listed throughout the paper with the values varying for different kinds of star, and different studies.

I know they can vary in size as they can be average or massive, so what is a size range for average stars and range for massive stars?

As well as depending on its mass, a star's radius also depends on its evolutionary stage. We usually describe stellar radii in terms of the sun's radius. At the moment, the sun's radius is obviously 1, but when it expands to become a giant star, it will be about 10 times the size. At the very end of its life, it will become an asymptotic giant branch star, with a radius around 200-300 times its current size. More massive stars are unsurprisingly larger, by generally not by more than a factor of 10 compared to the sun at each evolutionary stage (i.e. 10 -> 100 -> 2000 solar radii). The least massive stars, which are the most common, have radii around 0.1 times that of the sun (around the size of Jupiter), and this radius is not predicted to change much over their very long lifetimes. The Wikipedia article on stellar evolution is a good overview - check the sources for more information.

What is the lifetime range of an average binary star system and a massive binary star system?

This is tricky, since it depends on the masses of both stars, and the size of the binary orbit. A decent rule of thumb is that stars have a lifetime of around 10 billion years * (M / Msun) -2.5 . So you could calculate that time for the less massive star in the binary. For the most massive stars, that time is a few million years for the least massive, it is around a trillion. The lifetime of the binary can be shorter than this if the orbit's semimajor axis is smaller than the maximum radius of one of the stars. This can lead to Roche-lobe overflow or common envelope evolution, during which the two stars can merge, or one of their envelopes can be stripped off and ejected. It's worth noting that there are plenty of �' binaries, consisting of white dwarfs, neutron stars, and black holes. Over very long timescales, their orbits shrink due to gravitational wave emission, eventually causing them to merge, which we can detect with interferometers like LIGO, VIRGO, and KAGRA. You can calculate the timescale with the formula here.

Is there any special thing that happens during the stellar nebula stage to form 2 stars?

This isn't really my area, but I think there's a fair amount of uncertainty about exactly how binaries are formed.

One way could be similar to planet formation in a circumstellar disc - essentially forming a planet so large that is becomes a star. You would expect these systems to have quite extreme (i.e. very small) mass ratios, though.

A second option is that the two stars formed separately, and were gravitationally captured into a closed orbit during an interaction with a third body. This is fairly unlikely to happen, though, except in areas with very high densities of stars.

The final (and generally accepted) way is by fragmentation of a collapsing gas cloud. If the cloud has too much angular momentum, it will be unable to fully collapse into a single star. Roughly speaking, as the cloud contracts, its rotation speed increases until centrifugal force will tears it into two pieces. Each of the pieces can then collapse to form a star (unless it still has too much angular momentum).


Mass Exchange in X-ray Binary Stars

It was not clear from the early X-ray observations of the sky just exactly what was the origin of the amazingly bright sources that were being detected. In the early 1970s, data from the Uhuru satellite resulted in the association of several of these X-ray sources with mass exchange occurring between a normal star and a compact object (such as a neutron star or black hole) in a bound system. Theoreticians had long before shown that material falling onto such an object would be an efficient producer of X-rays.

Mass exchange in a binary system can occur by three modes:

    Roche-lobe overflow of the primary

For a low-mass X-ray binary (LMXRB, where a compact object is bound to a star whose mass is similar to or less than that of our Sun), the only way to achieve enough mass transfer to create large fluxes of X-rays is through Roche-lobe overflow. The Roche-lobe is the location between the two stars in a binary where the gravitational pull from one star is equal and opposite that of the other star. If the binary system is "close", i.e. the orbital radius is small, this point can occur near the surface of the normal star. Thus a "funnel point" is created for significant mass to flow out toward the compact star for accretion. In the case of Roche-lobe overflow, the angular momentum of the accreting material will tend to form a differentially rotating disk around the secondary. The material in this accretion disk is then slowly spiraled into the intense gravitational well of the compact object. It heats up to temperatures over 1,000,000 degrees and, therefore, shines brightly in X-rays.

A number of X-ray binaries are known to consist of a massive primary emitting a stellar wind driven by the primary's radiation pressure, orbited by a neutron star or black hole. Such a system is called a HMXRB, or high-mass X-ray binary the primary typically has a mass 10 times or more than that of our Sun. The compact object captures a fraction of the wind and converts the potential energy of the accreted plasma into X-rays. While qualitatively feasible, X-ray production by accretion from an undisturbed spherical wind can fall several orders of magnitude below the observed luminosity in the case of some binary systems ( e.g. , SMC X-1 and Cen X-3). However, simple modifications to the basic theory brought the observations closer to prediction. Such modifications include the effect of the X-ray emission on the velocity of the incoming wind and an angular dependence of the primary's mass loss.

In a Be star/neutron star binary, the behavior of the Be star controls the X-ray characteristics of the system. A Be star is a B star that rotates so rapidly that an instability results by which material streams out from the equatorial plane and an expanding atmosphere is formed. This introduces strong emission lines of hydrogen and neutral helium into the stellar spectrum. Furthermore, these stars are known to throw off large amounts of matter from their equatorial regions at apparently random intervals. The capture and accretion of this material by the secondary is known to be the source of many of the observed X-ray transients.


Binary star not exceeding Roche Lobe? - Astronomy

The formation of flows in the vicinity of the inner Lagrangian point has been computed for various close binary systems (from short-period U Gem to long-period β Lyr systems). The dependence of the masstransfer rate through the inner Lagrangian point on the degree of Roche-lobe overflow is derived. One new aspect of this work is the use of Kurucz stellar model atmospheres when constructing the initial configuration of the outer layers of the mass-losing star and also the use of the “large particles” numerical method of Belotserkovski and Davydov. The application of these stellar model atmospheres provides a more realistic description of the stream than do polytropic models. The computations show that the influence of the Coriolis and centrifugal forces on the rate of mass transfer is negligible and does not exceed a few percent. In certain specific cases (β Per and W UMa), the stream models differ strongly from those of Lubow and Shu. The degree of Roche-lobe overflow and the rate of mass transfer indicated by observations are such that the atmospheric layers of the mass-losing star are nearly always located at the inner Lagrangian point. The only exceptions are compact binary systems and U Gem stars, in which the inner Lagrangian point resides in layers of the mass-losing star that are denser than its atmospheric layers, and the β Per system, in which the mass-losing atmosphere is located inside its Roche lobe. The numerical dependences of the mass-transfer rate on the degree of Roche-lobe overflow differ from the analytical dependences for both large and small overflows. This is due to differences between the Kurucz model stellar atmospheres and the polytropic models used in previous analytical calculations and also to the presence of dynamical effects connected with the mass transfer in the computations. The polytropic indices corresponding to the best agreement between the numerical and analytical dependences are 4.5 for β Lyr, 2.4 2.6 for the cataclysmic binaries, and 3.1 3.3 for the remaining stars. These polytropic indices indicate that the Roche lobes of the mass-losing stars in close binary systems are usually overflowing.


Evolution of Cataclysmic Variables

While massive stars end their lives with a bang, low-mass stars end theirs with a whimper. Thermonuclear fusion in a low-mass star does not end with the total exhaustion of the star's thermonuclear fuel and the subsequent collapse of the star's core, as it does in a large star, but with the formation of a stable core that supports itself against gravity through the pressure exerted by degenerate electrons. The gentle transition from a hot core supported by thermal pressure to a cold core supported by degeneracy pressure preserves the mass of the star.

This evolution of the low-mass star makes the evolution of a compact binary system containing two low-mass stars a rather simple process. The transition from a system containing two fusion-powered stars to a system containing one fusion-powered star and one degenerate dwarf star does not disrupt the binary system, because the transition does not cause the system to lose mass. Even earlier in the evolution, where the more massive star losses a small quantity of gas when it transitions from hydrogen fusion to helium fusion, the amount of mass loss is small compared to the mass of the star, so the binary system is not disrupted. This makes the evolution of a binary system containing two low-mass star fundamentally different from a system containing at least one high-mass star in those systems, the mass lost by the high-mass star during a supernova is sufficient to disrupt the binary system.

With two low-mass stars, the star with more mass ends it life of thermonuclear fusion first, becoming a degenerate dwarf. Its companion star remains on the main-sequence, since its life of thermonuclear fusion is much longer. If the system is born with the stars close enough together, the orbit can decay enough to cause the main-sequence star to overflow its Roche lobe, dumping gas onto the degenerate dwarf. This transfer of mass from one star to the other is stable, because the mass flow is from the lower-mass star to the higher-mass star. We see these systems as cataclysmic variables.

Cataclysmic variables are driven by the loss of angular momentum and energy from their orbit. The loss is necessary, because the natural reaction of the binary system to mass transfer from the lower mass star to the higher mass star is to widen the separation between the stars, while the natural reaction of the mass donor is to shrink in radius. The loss of orbital angular momentum and energy causes the binary system to shrink rather than expand as mass transfer occurs, so that the main sequence star continues to overflow its Roche lobe. The interesting point about Roche Lobe overflow is that it locks the separation of the stars and the period of the binary orbit to the mass of the donor star in a predictable way. If the main-sequence star changes its character at a particular mass, it also changes its character at a particular orbital period.

Two mechanisms drive the loss of orbital energy and angular momentum. The first is gravitational radiation. As described elsewhere, this mechanism is important when the two stars are very close together. Farther apart, however, another mechanism is at work that drives the stars together in a reasonable time (less than the remaining lifetime of fusion-powered star). This mechanism is thought to be a stellar wind driven from the main-sequence star. We know that many stars have winds, including our own Sun. If the wind carries a magnetic field, it can extract a considerable amount of angular momentum from a binary system, because the torque exerted by the gas flowing away from the star is exerted back onto the star by the magnetic field. This lost angular momentum and energy comes from the binary system as a whole, because the degenerate dwarf exerts a torque on the main sequence star's Roche lobe that causes the main-sequence star to rotate synchronously with its orbit around the degenerate dwarf.

The loss of mass by the main sequence star is rapid enough to prevent the star from maintaining the stable configuration it would have away from a binary system. The reason is that the star loses mass faster than energy within the star can diffuse through the star, so the temperature gradient near the surface becomes steeper than it would be in an isolated main-sequence star. The effect of this is to cause the donor star to puff-up larger than it would be if isolated.

Cataclysmic variables begin their lives with long orbital periods, and evolve to shorter periods. The systems we see have periods ranging from as high as 15 hours to as low as 80 minutes. We don't see systems orbiting with periods shorter than 80 minutes. More unusual, we see very few cataclysmic variables with periods between 2 and 3 hours.

This period gap is thought to be caused by the shutting-down of the stellar wind, which dramatically slows the loss of orbital energy and angular momentum from the system. The decay of the binary orbit therefore slows, and the donor star suddenly has enough time to come into thermal equilibrium. This causes the star to shrink back to its normal main-sequence radius, ending mass transfer to the companion. The binary system remains invisible to us until the orbit shrinks enough to case the star to again overflow its Roche lobe. In this picture, the stellar wind ceases when the binary period is 3 hours, and Roche lobe overflow recommences when the binary period is 2 hours. Because the period of the system is tied by the Roche lobe overflow to the mass of the donor star, the wind ceases when the donor falls to a certain mass.

Below the period gap, the donor star continues to shrink as it loses mass until the electrons at its core become degenerate. When this occurs, the core of the star supports itself against gravity through degeneracy pressure rather than through thermal pressure. This changes how the star responds as it loses mass. In this state, the star expands rather than contracts as it loses mass. The binary system's reaction to mass transfer is naturally to expand, so the donor star's expansion can be accommodated the binary system, however, reacts to the mass transfer by increasing the separation between the donor star and the degenerate dwarf, which increases the orbital period. This mechanism gives the cataclysmic variables its minimum orbital period, which is observed at around 80 minutes.

Cataclysmic variables have two possible ends, one violent, the other quiet. The transfer of mass from the main-sequence star to the degenerate dwarf can push the degenerate dwarf over the Chandrasekhar limit, creating a type 1a supernova. This end can occur any time during the binary system's evolution. The other end is to simply disappear from sight, which occurs if there is insufficient mass in the main-sequence star to implode the degenerate dwarf. As the mass of the main-squence star drops, the center of mass of the system moves towards the more-massive degenerate dwarf, making gravitational radiation less efficient at removing orbital energy and angular momentum from the system. This causes mass transfer to slow to the point that the system becomes invisible. Eventually mass transfer stops as the donor star grows cold and crystallizes.